Nonlinear dynamical feedback for motion control of magnetic levitation system

For fast, nonlinear and unstable dynamical systems, such as magnetic levitation, high quality of control is essential. Such control can be generated by different feedback structures, most of which require measurements of velocities or derivatives of the system output. In case of magnetic levitation the velocity of levitating object (a ferromagnetic sphere) is not measured. That is the reason for application of state observers which along with different controllers will create a nonlinear dynamical feedback structure. In this paper we will consider two such structures - PID controller with a nonlinear feed-forward and a cascade linearising feedback using two nonlinear state observers: High-Gain observer (HGO) and an observer with reduced, linear error dynamics (abbreviated as RO). Operation of these control algorithms will be compared with a classical PID structure, derivative part of which will be realised either as a finite difference or with an observer.